I think this project seems valuable for three main reasons:

1. It would provide a test of dual-use research (DUR) policies and policy implementation, improving future efforts to limit the publication of DUR. Indeed, if the project succeeds, it is likely to provide a blueprint for future action that can be easily replicated with journals and other preprint servers. If it fails, it will yield valuable information about what our blindspots are and what types of projects we should pursue in the future. As far as I know, the EA biosecurity community has not yet tried working directly with publishers.
2. It would normalize responsible publication (as opposed to maximal openness) and raise awareness of dual-use concerns within the scientific community, making future efforts to limit the publication of DUR more likely to succeed.
3. In some (very rare) scenarios, it might actually limit the spread of dangerous information. Journals tend to have better review processes than preprint servers, so it is possible to imagine a particularly dangerous piece of research (e.g., the creation of a new superbug) being denied publication in a journal only to find that it has spread widely over the internet after being submitted to arXiv.org.

Additionally, it is clear that servers like arXiv.org are highly resource-constrained (see https://www.scientificamerican.com/article/arxiv-org-reaches-a-milestone-and-a-reckoning/).

With that said, striking the right balance between openness and security is difficult, and this project might generate significant backlash or have unintended consequences. I wrote up some additional thoughts about this project after discussing it with Yonatan, so please reach out to me if you would like to read more about what this project might look like and why it might or might not be a good idea.

I would say two things about this.

1. This project is still in the early stages, and I have not yet developed a concrete hypothesis about what would constitute "good guidelines that a) reduce GCBR and b) preprint servers will approve of." arXiv and other servers already use humans to do some basic vetting, so expanding their mandate to cover dual use issues is an option, but there may be cheaper things (like researcher self-certification) to try first.
2. Once I have a hypothesis that other EA biosecurity people agree is worth testing, the next step is getting in touch with preprint server administrators and users to see what they think. This should help answer the other questions you raise.

EDIT: I am no longer leading this project, and after talking to a few biosecurity professionals, the project is on hold.